Question: Solve for $x$ : $5x^2 + 55x + 90 = 0$
Solution: Dividing both sides by $5$ gives: $ x^2 + {11}x + {18} = 0 $ The coefficient on the $x$ term is $11$ and the constant term is $18$ , so we need to find two numbers that add up to $11$ and multiply to $18$ The two numbers $9$ and $2$ satisfy both conditions: $ {9} + {2} = {11} $ $ {9} \times {2} = {18} $ $(x + {9}) (x + {2}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 9) (x + 2) = 0$ $x + 9 = 0$ or $x + 2 = 0$ Thus, $x = -9$ and $x = -2$ are the solutions.